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process has a linear dependence on the ambient magnetic field strength if the growth rate of the CR’s energy is limited by its Larmor radius (Lagage and Cesarsky 1983). Under this assumption strengths of ∼ 10 −10 G are necessary to accelerate a CR to 10 9 eV (Zweibel 2003). The strength, generation, and dispersal of magnetic fields at high redshifts, however, is still highly uncertain. One of the most widely held views is that magnetic seed fields were created soon after the Big Bang and were later amplified in higher-density structures through dynamo mechanisms. Seed fields are thought to form through various processes including galaxy-scale outflows in the early Universe and the Biermann battery mechanism in regions such as shock waves and ionization fronts (e.g. Kronberg et al. 1999; Gnedin et al. 2000). For one illustrative example, Ichiki et al. 2006 propose a mechanism by which seed fields are created before recombination through second-order cosmological perturbations. They calculate the seed field at the redshift of recombination, zrec ≈ 1000, to be B0(zrec) 10 −14 G λ 10 kpc −2 , (6.16) where λ is the comoving size of the structure in question for scales less than about 10 Mpc. If we take into account magnetic flux freezing as structures become dense and the Universe expands, we get a seed field at virialization of B0(zvir) 10 −20 G λ 10 kpc −2 ρs ρo 2/3 (1 + zvir) zvir 2 , (6.17) where (ρs/ρo)zvir ∼ 200 is the overdensity of the structure in question com- pared to the average density of the Universe at zvir, the redshift at which the structure first virializes. For a minihalo with a comoving size of around 10 kpc 154
and virialization redshift zvir = 20, this gives B0 ∼ 10 −16 G. When dynamo effects are taken into account, the magnetic field is further amplified and can grow exponentially on a timescale determined by differential rotation and tur- bulence within the structure (e.g. Field 1995; Widrow 2002). Magnetic field amplification within the accelerating region of a SN remnant itself may also increase its strength by up to two orders of magnitude (e.g. van der Laan 1962; Bell and Lucek 2001). This magnetic field growth can occur through processes such as flux freezing in the compressed regions of the SN remnant and non-linear amplification through growth and advection of Alfvén waves generated by the pressure of CRs themselves. Within structures that have already experienced star formation, magnetic fields can further be built up through field ejection in stellar winds, SN blastwaves, and protostellar jets (e.g. Machida et al. 2006). For these fields to be spread into the general IGM, however, there must be a sufficient degree of turbulent mixing and diffusion in intergalactic regions. While such processses are effective within structures, it is less obvious that they are also effective in the IGM at eras soon after star formation has begun (Rees 2006). Thus, the build-up and amplification of magnetic fields in pristine intergalactic matter and in the filaments at high redshifts is very uncertain. We can estimate the critical magnetic field at z ∼ 20 that would influence CR propagation by equating the relevant physical distance scale with the Larmor radius rL and finding the corresponding magnetic field strength, where for a proton rL = γmHβc 2 /(eB), and e is the proton charge. Considering the maximum scale a CR could travel at z ∼ 20, we write rL = βc/H(z = 20), where βc is the CR velocity and H(z) the Hubble constant at redshift z. For ɛCR = 10 6 eV, we find rL 90 Mpc, corresponding to a magnetic field strength 155
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Copyright by Athena Ranice Stacy 20
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New Insights into Primordial Star F
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Acknowledgments I first want to giv
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angular momentum to rotate at nearl
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2.4.2.5 Thermodynamics of accretion
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Chapter 7. Outlook 177 Bibliography
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List of Figures 2.1 Density project
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1.1 Motivation Chapter 1 Introducti
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leaving behind a neutron star or bl
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describe studies that have attempte
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CRs may therefore provide a pathway
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expected that some of the gas withi
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our numerical methodology in Chapte
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scattering is the major source of o
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portance. The reaction rates for an
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The size of the refinement levels h
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the sink a temperature and pressure
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same time, such as the fragments in
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Figure 2.2: Physical state of the c
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2.4.2 Protostellar accretion 2.4.2.
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Despite some amount of rotational s
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Figure 2.6: Velocity field of the c
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Figure 2.7: Disk mass vs. time sinc
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Figure 2.8: Angular momentum struct
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sink tform [yr] Mfinal [M⊙] rinit
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sink (∼ 4 M⊙) that merged with
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actual final mass of the star is li
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the average temperature of all part
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disk accretion onto a primordial pr
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Figure 2.12: Impact of feedback on
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Figure 2.13: Comparison of specific
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the central core, eventually compri
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extending our simulation to later t
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that such a non-primordial origin t
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impose an upper mass limit to Pop I
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we use a ray-tracing scheme to foll
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3.2.3 Sink Particle Method When an
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convenient way to directly measure
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where the sum now extends from the
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Figure 3.1: Evolution of various pr
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ased on the prescription of Omukai
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ate found at late times in our ‘n
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Figure 3.2: Evolution of various di
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Figure 3.3: Evolution of disk mass
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Figure 3.4: Temperature versus numb
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disk mass is able to level off in d
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Figure 3.6: Projected density and t
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onto the disk. The numerical experi
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that the I-front expands as an hour
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Figure 3.8: Evolution of various H
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˙ M∗ = 3πΣν, (3.18) where ν
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the discrete nature of the gas part
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stars. We also note that, despite t
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current computational limits. If ra
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the deaths of massive stars (see Wo
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It is apparent that the angular mom
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h = 0.7. To accelerate structure fo
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acc = Lres 50 AU, where: Lres 0.5
Page 117 and 118: years, up to several dynamical time
Page 119 and 120: sp = GM∗ c2 , (4.1) s where cs is
Page 121 and 122: Figure 4.2: Left: Angular momentum
Page 123 and 124: through the disk, and the disk is e
Page 125 and 126: steadily grows for the rest of the
Page 127 and 128: Fig. 4.5 shows these timescales for
Page 129 and 130: sink B. Once on the MS, the sink A
Page 131 and 132: Figure 4.6: Evolution of stellar ro
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Page 135 and 136: present here, particularly if the s
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Page 141 and 142: which has already detected GRBs at
Page 143 and 144: M⊙. They find that the specific a
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Page 149 and 150: Figure 5.1: Top panels: Effective v
Page 151 and 152: Figure 5.2: Effect of relative stre
Page 153 and 154: Using cs ∝ T 1/2 results in ρ
Page 155 and 156: Figure 5.4: Evolution of gas proper
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Page 159 and 160: abundances of HD, which also acts a
Page 161 and 162: first stars had very short lifetime
Page 163 and 164: of star-forming material. Here we t
Page 165 and 166: star formation, they found CR energ
Page 167: The GZK cutoff applies only to thos
Page 171 and 172: and undergoes free-fall collapse. I
Page 173 and 174: β = 1 − −2 1/2 ɛ + 1 mHc2
Page 175 and 176: and where ΓCR(D) = 5 × 10 −29 e
Page 177 and 178: Figure 6.2: Thermal evolution of pr
Page 179 and 180: Figure 6.3: Minimum temperature rea
Page 181 and 182: Figure 6.4: Thermal evolution of pr
Page 183 and 184: The CR energy density can now be es
Page 185 and 186: 2007). When considering realistic c
Page 187 and 188: 6.3.5 Fragmentation scale As is evi
Page 189 and 190: 2006). This decrease in fragmentati
Page 191 and 192: Chapter 7 Outlook Our understanding
Page 193 and 194: that Pop III stars likely experienc
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Page 197 and 198: Barkana, R. and Loeb, A. (2001). In
Page 199 and 200: Bromm, V., Kudritzki, R. P., and Lo
Page 201 and 202: Daigne, F., Olive, K. A., Silk, J.,
Page 203 and 204: Gao, L., White, S. D. M., Jenkins,
Page 205 and 206: Heger, A., Woosley, S. E., and Spru
Page 207 and 208: Kratter, K. M. and Murray-Clay, R.
Page 209 and 210: Machida, M. N., Omukai, K., Matsumo
Page 211 and 212: Navarro, J. F. and White, S. D. M.
Page 213 and 214: Rollinde, E., Vangioni, E., and Oli
Page 215 and 216: Simon, M., Ghez, A. M., Leinert, C.
Page 217 and 218: Tanvir, N. R., Fox, D. B., Levan, A
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Rays, volume 576 of Lecture Notes i
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Zatsepin, G. T. and Kuz’min, V. A
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